Its simple.

Find the period of any functn whose period is not known by putting value.

eg:{5.6}=0.6={6.6}={7.6}

Hence the period of {x}=1.

f(x+T)=f(x),then of all possible values of T,
the least value is period.

for trignometric functions with mod sinx period is ,you can also try substitution.

mostly they are pi,pi/2,2pi